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Fast integer multiplication using genera...
Covanov, Svyatoslav...

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Fast integer multiplication using generalized Fermat primes by Covanov, Svyatoslav ( Author )
Lemonjar Open Access
Australian National University
07-09-2023
For almost 35 years, Sch{\"o}nhage-Strassen's algorithm has been the fastest algorithm known for multiplying integers, with a time complexity O(n $\times$ log n $\times$ log log n) for multiplying n-bit inputs. In 2007, F{\"u}rer proved that there exists K > 1 and an algorithm performing this operation in O(n $\times$ log n $\times$ K log n). Recent work by Harvey, van der Hoeven, and Lecerf showed that this complexity estimate can be improved in order to get K = 8, and conjecturally K = 4. Using an alternative algorithm, which relies on arithmetic modulo generalized Fermat primes, we obtain conjecturally the same result K = 4 via a careful complexity analysis in the deterministic multitape Turing model.
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English
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MYR 0.01
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http://arxiv.org/abs/1502.02800
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